gftool.basis.pole

Representation using poles and the corresponding residues.

Assuming we have only simple poles Green’s functions, we can represent Green’s functions using these poles and their corresponding residues:

\[g(z) = \sum_j r_j / (z - ϵ_j)\]

where \(ϵ_j\) are the poles and \(r_j\) the corresponding residues. Self-energies can also be represented by the poles after subtracting the static part.

The pole representation is closely related to the Padé approximation, as rational polynomials with numerator degree N bigger then dominator degree M, can also be represented using M poles.

API

Functions

gf_d1_z(z, poles, weights)	First derivative of Green's function given by a finite number of poles.
gf_from_moments(moments[, width])	Find pole Green's function matching given moments.
gf_from_tau(gf_tau, n_pole, beta[, moments, ...])	Find pole Green's function fitting gf_tau.
gf_from_z(z, gf_z, n_pole[, moments, width, ...])	Find pole causal Green's function fitting gf_z.
gf_ret_t(tt, poles, weights)	Retarded time Green's function given by a finite number of poles.
gf_tau(tau, poles, weights, beta)	Imaginary time Green's function given by a finite number of poles.
gf_z(z, poles, weights)	Green's function given by a finite number of poles.
moments(poles, weights, order)	High-frequency moments of the pole Green's function.

Classes

PoleFct(poles, residues)	Function given by finite number of simple poles and residues.
PoleGf(poles, residues)	Fermionic Green's function given by finite number of poles and residues.